Addition of Rational Numbers with Different Denominator

Let us discuss in detail How to Add Rational Numbers with Different Denominators. To find the Sum of Rational Numbers you can have a look at the below examples provided. Check the detailed procedure to add rational numbers not having the common denominator.

How to Add Rational Numbers with Different Denominators?

Go through the below-mentioned steps to add rational numbers having different denominators. They are along the lines

Step 1: Check the Rational Numbers and see whether the denominators are positive or not. If any of the denominators is negative rearrange them to become positive.

Step 2: List out the denominators of rational numbers in the earlier step.

Step 3: Determine the LCM of the denominators of the given Rational Numbers.

Step 4: Express the Rational Numbers in a way that they have the Common Denominator using the LCM obtained.

Step 5: Write down the numerator as the sum of numerators of rational numbers obtained in the earlier step and denominators is the LCM obtained in Step 3.

Step 6: Rational Number obtained in Step 5 is the required sum and simplify if required.

Solved Examples on Adding Rational Numbers with Different Denominator

1.  Add Rational Numbers -8/21 and 3/9?

Solution:

Given Rational Numbers are -8/21, 3/9

= -8/21+3/9

Firstly, find the Least Common Multiple of the Denominators i.e. 21, 9

LCM(21, 9) = 63

Express the Rational Numbers with Common Denominator using the LCM Obtained.

-8/21 = -8*3/21*3 = -24/63

3/9 = 3*7/9*7 = 21/63

Adding them we get

-24/63+21/63

= (-24+21)/63

= -3/63

Simplifying further we get -1/21

Therefore the Sum of -8/21 and 3/9 is -1/21.

2. Add 3/4 and 5?

Solution:

Given Rational Numbers are 3/4 and 5/1

= 3/4+5/1

Find the LCM of 4, 1

LCM(4, 1) = 4

Express the Given Rational Numbers in terms of Common Denominator using the LCM obtained.

3/4 = 3*1/4*1 = 3/4

5/1 = 5*4/1*4 = 20/4

Add the obtained rational numbers numerators with a common denominator

= (3+20)/4

= 23/4

Therefore, the Sum of 3/4 and 5 is 23/4.

3. Simplify 5/-12+7/-4?

Solution:

Given Rational Numbers are 5/-12 and 7/-4

Since the rational numbers are having a negative denominator rearrange them to have a positive denominator.

5/-12 = 5*(-1)/-12*(-1) = -5/12

7/-4 = 7*(-1)/-4*(-1) = -7/4

Find the LCM of Denominators of the Rational Numbers.

LCM(12, 4) = 12

Express the Rational Numbers with Common Denominator using the LCM obtained.

-5/12 = -5*1/12*1 = -5/12

-7/4= -7*3/4*3 = -21/12

Add the Obtained Rational Numbers Numerators and keep the denominator unchanged.

= (-5-21)/12

= -26/12

Thus, 5/-12+7/-4 is -26/12.